Question: Cedric has deposited $\$12,\!000$ into an account that pays $5\%$ interest compounded annually.

Daniel has deposited $\$12,\!000$ into an account that pays $7\%$ simple annual interest.

In $15$ years Cedric and Daniel compare their respective balances. To the nearest dollar, what is the positive difference between their balances?
Solution: We may find Cedric's balance by simply finding $\$12,\!000(1 + 0.05)^{15} \approx \$24,\!947.14.$

We may find Daniel balance by finding $\$12,\!000(1 + 15 \cdot 0.07) \approx \$24,\!600.$

Therefore, the difference between their balances is roughly $\$24,\!947.14 - \$24,\!600 \approx \boxed{\$347}.$